\newproblem{lay:7_4_3}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 7.4.3}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Find the singular values of the matrix $A=\begin{pmatrix}\sqrt{6} & 1 \\ 0 & \sqrt{6}\end{pmatrix}$
}{
   % Solution
	We compute $A^TA$
	\begin{center}
		$A^TA=\begin{pmatrix}\sqrt{6} & 0 \\ 1 & \sqrt{6}\end{pmatrix}\begin{pmatrix}\sqrt{6} & 1 \\ 0 & \sqrt{6}\end{pmatrix}=
		   \begin{pmatrix}6 & \sqrt{6} \\ \sqrt{6} & 7\end{pmatrix}$
	\end{center}
	whose eigenvalues are
	\begin{center}
		$\lambda_1=9$ \\
		$\lambda_2=4$ \\
	\end{center}
	The singular values of $A$ are
	\begin{center}
		$\sigma_1=\sqrt{\lambda_1}=3$ \\
		$\sigma_2=\sqrt{\lambda_2}=2$ \\
	\end{center}
}
\useproblem{lay:7_4_3}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}

